Study Of The Topology And Phase Transition Propertys In One-dimensional Non-hermitian Quantum Systems

This thesis mainly investigates the topology and phase transition in one-dimensional(1D)non-Hermitian quantum systems.We discuss the influences of the non-Hermitian terms to the original systems in several kinds of specific models.First,we explore the relationship between complex geometry phases,topology and PT-symmetry breaking by studying a general PT-symmetry two-level(band)model.The complex geometry phase is evaluated in the unbroken PT-symmetry region and the physical meaning of the real(imaginary)part of complex geometry is discussed.Two concrete models are given to exemplify the property of the complex geometry phase,one is a Wu–Qi-Zhang like PT symmetrical Hamiltonian,the other is a kind of PT-symmetrical Su-Schrieffer-Heeger(SSH)model with gain and loss in every sublattice.Then,we discuss the effects of another non-Hermitian mechanism called asymmetrical hopping in one-dimensional lattice systems.The study of the non-Hermitian simple lattice shows that the asymmetrical hopping may lead to non-Hermitian skin effect in one-dimensional lattice systems.For the SSH model with asymmetrical hopping,the nonHermitian skin effect changes the topology of the original system dramatically,which results in the failure of conventional bulk-edge correspondence.By defining the non-Bloch Hamiltonian,the bulk-edge correspondence relation can recovered in the non-Hermitian system.We also discuss the condition of producing the continuum bands in a general one-dimensional non-Hermitian tight binding model.Besides,we study the effects of dissipative term on quantum phase transition and mainly focus on an one dimensional non-Hermitian quantum XY model with complex transverse field.The many-body spectrum is obtained analytically and the influence of non-Hermitian term on phase diagram is explored.By the geometry phase approach,we also analyze the effects of imaginary transverse field on the hehavoir of quantum critical in different interaction region.Finally,the influences of asymmetrical coupling on Bose–Einstein condensation is explored.we mainly discuss a kind of non-Hermitian Bose–Hubbard dimer.Through Schwinger representation,this boson model can be mapped to a angular momentum model.Employing a mean field approximation for the generalized SU(2)coherent state can get the non-Hermitian Bloch dynamical evolution equation and discrete GrossPitaevskii type Schrodinger equation.We also discuss the generalized conical structure and solve the fixed points of the dynamical evolution equation.